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<div class="subTitle">org.apache.commons.math3.fitting.leastsquares</div>
<h2 title="Class LevenbergMarquardtOptimizer" class="title">Class LevenbergMarquardtOptimizer</h2>
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<dd><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer</a></dd>
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<pre>public class <span class="strong">LevenbergMarquardtOptimizer</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer</a></pre>
<div class="block">This class solves a least-squares problem using the Levenberg-Marquardt
 algorithm.

 <p>This implementation <em>should</em> work even for over-determined systems
 (i.e. systems having more point than equations). Over-determined systems
 are solved by ignoring the point which have the smallest impact according
 to their jacobian column norm. Only the rank of the matrix and some loop bounds
 are changed to implement this.</p>

 <p>The resolution engine is a simple translation of the MINPACK <a
 href="http://www.netlib.org/minpack/lmder.f">lmder</a> routine with minor
 changes. The changes include the over-determined resolution, the use of
 inherited convergence checker and the Q.R. decomposition which has been
 rewritten following the algorithm described in the
 P. Lascaux and R. Theodor book <i>Analyse num&eacute;rique matricielle
 appliqu&eacute;e &agrave; l'art de l'ing&eacute;nieur</i>, Masson 1986.</p>
 <p>The authors of the original fortran version are:
 <ul>
 <li>Argonne National Laboratory. MINPACK project. March 1980</li>
 <li>Burton S. Garbow</li>
 <li>Kenneth E. Hillstrom</li>
 <li>Jorge J. More</li>
 </ul>
 The redistribution policy for MINPACK is available <a
 href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it
 is reproduced below.</p>

 <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
 <tr><td>
    Minpack Copyright Notice (1999) University of Chicago.
    All rights reserved
 </td></tr>
 <tr><td>
 Redistribution and use in source and binary forms, with or without
 modification, are permitted provided that the following conditions
 are met:
 <ol>
  <li>Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.</li>
 <li>Redistributions in binary form must reproduce the above
     copyright notice, this list of conditions and the following
     disclaimer in the documentation and/or other materials provided
     with the distribution.</li>
 <li>The end-user documentation included with the redistribution, if any,
     must include the following acknowledgment:
     <code>This product includes software developed by the University of
           Chicago, as Operator of Argonne National Laboratory.</code>
     Alternately, this acknowledgment may appear in the software itself,
     if and wherever such third-party acknowledgments normally appear.</li>
 <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
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     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
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 </table></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.3</dd>
<dt><span class="strong">Version:</span></dt>
  <dd>$Id: LevenbergMarquardtOptimizer.java 1573308 2014-03-02 14:02:50Z luc $</dd></dl>
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<h3>Nested classes/interfaces inherited from interface&nbsp;org.apache.commons.math3.fitting.leastsquares.<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer</a></h3>
<code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.Optimum.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer.Optimum</a></code></li>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#LevenbergMarquardtOptimizer()">LevenbergMarquardtOptimizer</a></strong>()</code>
<div class="block">Default constructor.</div>
</td>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#LevenbergMarquardtOptimizer(double, double, double, double, double)">LevenbergMarquardtOptimizer</a></strong>(double&nbsp;initialStepBoundFactor,
                           double&nbsp;costRelativeTolerance,
                           double&nbsp;parRelativeTolerance,
                           double&nbsp;orthoTolerance,
                           double&nbsp;qrRankingThreshold)</code>
<div class="block">Construct an instance with all parameters specified.</div>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#getCostRelativeTolerance()">getCostRelativeTolerance</a></strong>()</code>
<div class="block">Gets the value of a tuning parameter.</div>
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<tr class="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#getInitialStepBoundFactor()">getInitialStepBoundFactor</a></strong>()</code>
<div class="block">Gets the value of a tuning parameter.</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#getOrthoTolerance()">getOrthoTolerance</a></strong>()</code>
<div class="block">Gets the value of a tuning parameter.</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#getParameterRelativeTolerance()">getParameterRelativeTolerance</a></strong>()</code>
<div class="block">Gets the value of a tuning parameter.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#getRankingThreshold()">getRankingThreshold</a></strong>()</code>
<div class="block">Gets the value of a tuning parameter.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.Optimum.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer.Optimum</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#optimize(org.apache.commons.math3.fitting.leastsquares.LeastSquaresProblem)">optimize</a></strong>(<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresProblem.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresProblem</a>&nbsp;problem)</code>
<div class="block">Solve the non-linear least squares problem.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withCostRelativeTolerance(double)">withCostRelativeTolerance</a></strong>(double&nbsp;newCostRelativeTolerance)</code>&nbsp;</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withInitialStepBoundFactor(double)">withInitialStepBoundFactor</a></strong>(double&nbsp;newInitialStepBoundFactor)</code>&nbsp;</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withOrthoTolerance(double)">withOrthoTolerance</a></strong>(double&nbsp;newOrthoTolerance)</code>
<div class="block">Modifies the given parameter.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withParameterRelativeTolerance(double)">withParameterRelativeTolerance</a></strong>(double&nbsp;newParRelativeTolerance)</code>&nbsp;</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withRankingThreshold(double)">withRankingThreshold</a></strong>(double&nbsp;newQRRankingThreshold)</code>&nbsp;</td>
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<h4>LevenbergMarquardtOptimizer</h4>
<pre>public&nbsp;LevenbergMarquardtOptimizer()</pre>
<div class="block">Default constructor.
 <p>
 The default values for the algorithm settings are:
 <ul>
  <li>Initial step bound factor: 100</li>
  <li>Cost relative tolerance: 1e-10</li>
  <li>Parameters relative tolerance: 1e-10</li>
  <li>Orthogonality tolerance: 1e-10</li>
  <li>QR ranking threshold: <a href="../../../../../../org/apache/commons/math3/util/Precision.html#SAFE_MIN"><code>Precision.SAFE_MIN</code></a></li>
 </ul></div>
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<h4>LevenbergMarquardtOptimizer</h4>
<pre>public&nbsp;LevenbergMarquardtOptimizer(double&nbsp;initialStepBoundFactor,
                           double&nbsp;costRelativeTolerance,
                           double&nbsp;parRelativeTolerance,
                           double&nbsp;orthoTolerance,
                           double&nbsp;qrRankingThreshold)</pre>
<div class="block">Construct an instance with all parameters specified.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>initialStepBoundFactor</code> - initial step bound factor</dd><dd><code>costRelativeTolerance</code> - cost relative tolerance</dd><dd><code>parRelativeTolerance</code> - parameters relative tolerance</dd><dd><code>orthoTolerance</code> - orthogonality tolerance</dd><dd><code>qrRankingThreshold</code> - threshold in the QR decomposition. Columns with a 2
                               norm less than this threshold are considered to be
                               all 0s.</dd></dl>
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<h4>withInitialStepBoundFactor</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a>&nbsp;withInitialStepBoundFactor(double&nbsp;newInitialStepBoundFactor)</pre>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>newInitialStepBoundFactor</code> - Positive input variable used in
 determining the initial step bound. This bound is set to the
 product of initialStepBoundFactor and the euclidean norm of
 <code>diag * x</code> if non-zero, or else to <code>newInitialStepBoundFactor</code>
 itself. In most cases factor should lie in the interval
 <code>(0.1, 100.0)</code>. <code>100</code> is a generally recommended value.
 of the matrix is reduced.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a new instance.</dd></dl>
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<h4>withCostRelativeTolerance</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a>&nbsp;withCostRelativeTolerance(double&nbsp;newCostRelativeTolerance)</pre>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>newCostRelativeTolerance</code> - Desired relative error in the sum of squares.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a new instance.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a>&nbsp;withParameterRelativeTolerance(double&nbsp;newParRelativeTolerance)</pre>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>newParRelativeTolerance</code> - Desired relative error in the approximate solution
 parameters.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a new instance.</dd></dl>
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<h4>withOrthoTolerance</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a>&nbsp;withOrthoTolerance(double&nbsp;newOrthoTolerance)</pre>
<div class="block">Modifies the given parameter.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>newOrthoTolerance</code> - Desired max cosine on the orthogonality between
 the function vector and the columns of the Jacobian.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a new instance.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html" title="class in org.apache.commons.math3.fitting.leastsquares">LevenbergMarquardtOptimizer</a>&nbsp;withRankingThreshold(double&nbsp;newQRRankingThreshold)</pre>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>newQRRankingThreshold</code> - Desired threshold for QR ranking.
 If the squared norm of a column vector is smaller or equal to this
 threshold during QR decomposition, it is considered to be a zero vector
 and hence the rank of the matrix is reduced.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a new instance.</dd></dl>
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<pre>public&nbsp;double&nbsp;getInitialStepBoundFactor()</pre>
<div class="block">Gets the value of a tuning parameter.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the parameter's value.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withInitialStepBoundFactor(double)"><code>withInitialStepBoundFactor(double)</code></a></dd></dl>
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<pre>public&nbsp;double&nbsp;getCostRelativeTolerance()</pre>
<div class="block">Gets the value of a tuning parameter.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the parameter's value.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withCostRelativeTolerance(double)"><code>withCostRelativeTolerance(double)</code></a></dd></dl>
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<pre>public&nbsp;double&nbsp;getParameterRelativeTolerance()</pre>
<div class="block">Gets the value of a tuning parameter.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the parameter's value.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withParameterRelativeTolerance(double)"><code>withParameterRelativeTolerance(double)</code></a></dd></dl>
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<pre>public&nbsp;double&nbsp;getOrthoTolerance()</pre>
<div class="block">Gets the value of a tuning parameter.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the parameter's value.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withOrthoTolerance(double)"><code>withOrthoTolerance(double)</code></a></dd></dl>
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<pre>public&nbsp;double&nbsp;getRankingThreshold()</pre>
<div class="block">Gets the value of a tuning parameter.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the parameter's value.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LevenbergMarquardtOptimizer.html#withRankingThreshold(double)"><code>withRankingThreshold(double)</code></a></dd></dl>
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<h4>optimize</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.Optimum.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer.Optimum</a>&nbsp;optimize(<a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresProblem.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresProblem</a>&nbsp;problem)</pre>
<div class="block">Solve the non-linear least squares problem.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.html#optimize(org.apache.commons.math3.fitting.leastsquares.LeastSquaresProblem)">optimize</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/fitting/leastsquares/LeastSquaresOptimizer.html" title="interface in org.apache.commons.math3.fitting.leastsquares">LeastSquaresOptimizer</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>problem</code> - the problem definition, including model function and
                            convergence criteria.</dd>
<dt><span class="strong">Returns:</span></dt><dd>The optimum.</dd></dl>
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